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          RL Summary 4 - Policy-Based Reinforcement Learning
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        <h1 id="策略函数-π-a-s"><a href="#策略函数-π-a-s" class="headerlink" title="策略函数: π(a|s)"></a>策略函数: π(a|s)</h1><p>策略函数的输入是当前状态S，输出是概率分布，即根据状态确定输出。我们需要用一个函数来近似策略函数，近似函数有很多种方法，可以用核函数，线性函数，也可以用神经网络。如果用神经网络来近似这个策略函数，那么我们把这个函数称为策略网络(Policy Network)，其表达式应满足<br>$$<br>\Sigma_{a\in A}\pi(a|s,\theta)&#x3D;1<br>$$<br>其中theta代表神经网络的参数。</p>
<h1 id="策略学习"><a href="#策略学习" class="headerlink" title="策略学习"></a>策略学习</h1><p>对动作价值函数求A的期望，即得到状态价值函数<br>$$<br>V_\pi(s_t)&#x3D;E_A[Q_\pi(s_t,A)]&#x3D;\Sigma_a\pi(a|s_t)*Q_\pi(s_t,a)<br>$$<br>接下来，就要用神经网络近似状态价值函数，即用策略函数替换为神经网络。此时状态价值函数应该是关于s和theta的函数，那么在状态价值函数中，对状态求期望，就能得到一个只和theta有关的函数：<br>$$<br>J(\theta)&#x3D;E_s[V(S;\theta)]<br>$$<br>那么我们的目标很明确了，通过改变theta，使函数J得到最大值。那么如何优化theta呢？使用策略梯度算法梯度上升优化theta。策略梯度算法分为两步：</p>
<ul>
<li><p>观察状态S</p>
</li>
<li><p>更新theta值：<br>$$<br>\theta&#x3D;\theta+\beta*{\partial V(s;\theta) \over \partial \theta}<br>$$</p>
</li>
</ul>
<h1 id="算法流程总结"><a href="#算法流程总结" class="headerlink" title="算法流程总结"></a>算法流程总结</h1><ul>
<li><p>获取状态S</p>
</li>
<li><p>由神经网络近似的π函数计算出a</p>
</li>
<li><p>计算行动价值函数，记为：<br>$$<br>q_t\approx Q_\pi(s_t,a_t)<br>$$</p>
</li>
<li><p>对策略网络π求导, tensorflow和pytorch都将这个函数封装好，可以直接调用：<br>$$<br>d_{\theta,t}&#x3D;{\partial log\pi(a_t|s_t,\theta) \over \partial\theta}|_{\theta&#x3D;\theta_t}<br>$$</p>
</li>
<li><p>近似地算策略梯度<br>$$<br>g(a_t,\theta_t)&#x3D;q_t*d_{\theta,t}<br>$$</p>
</li>
<li><p>更新策略网络<br>$$<br>\Theta_{t+1}&#x3D;\Theta_t+\beta*g(a_t,\Theta_t)<br>$$</p>
</li>
</ul>
<p>在上述流程中，如何近似地计算行动价值函数qt呢，有两种算法：</p>
<ol>
<li>REINFORCE算法<br>在一次完整的训练结束后，即在围棋中，一局完整的棋局结束后，计算所有的折扣汇报之和ut，并使用ut作为行动价值函数qt的近似值</li>
<li>用神经网络做近似<br>原本已经用了神经网络近似函数π，现在用另一个神经网络近似qt。这两个神经网络一个被称为actor，一个被称为critic，这种方法被称为actor-critic方法。</li>
</ol>
<blockquote>
<p>本文内容为Shusen Wang老师深度强化学习系列课程的学习笔记 视频：<a target="_blank" rel="noopener" href="https://youtu.be/vmkRMvhCW5c">https://youtu.be/vmkRMvhCW5c</a> 课件：<a target="_blank" rel="noopener" href="https://github.com/wangshusen/DeepLearning">https://github.com/wangshusen/DeepLearning</a></p>
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